Pressure sensitive surfaces

ABSTRACT

A position sensor comprises a substrate having an array of pressure sensors and a membrane overlying the substrate. The membrane includes physical parameters which vary with position. The membrane may include discontinuous regions and protrusions which affect the way in which forces on the membrane are distributed to the substrate. A pressure sensor may also include a controller for receiving pressure information from the substrate, with a signal processor being programmed to localize the depressed region or regions of the substrate.

CROSS-REFERENCE TO RELATED APPLICATION

This is a Continuation of application Ser. No. 10/184,080, filed on 28Jun. 2002 now U.S. Pat. No. 6,715,359, and entitled PRESSURE SENSITIVESURFACES, which also claims the benefit of U.S. Provisional ApplicationNo. 60/301,238, filed Jun. 28, 2001.

TECHNICAL FIELD

This invention relates to pressure-sensitive devices. More particularly,the invention concerns structures for accurately localizing pointsources of pressure and methods for determining the location and forceof a point pressure source on a pressure-sensing surface. The inventionmay be applied to provide interfaces to electronic devices.

BACKGROUND

It is known to make pressure-sensitive surfaces by instrumenting a mator other structure which includes a surface region with an array ofpressure sensing elements. For example, an array of pressure sensors ofthe type described in PCT publication No. WO 99/04234 (Reimer, et al.),can be used to detect the location and pressure applied by severalsimultaneous points of contact.

The surface may be covered with a membrane as described, for example, inWO 00/73982 (Inkster). Such membranes can cause problems, however. Amembrane can distribute pressure so that touching at one location causessignals from the pressure sensors in a surrounding area. The priorpressure-sensitive surfaces described above provide no way to isolatethe response of a set of pressure sensors from neighboring ones.

In conventional pressure-sensitive structures which include a membraneoverlying an array of pressure sensors, the membrane distributespressure imposed by an indentor radially outwardly from the indentor ina generally uniform manner. The inventors have determined that byselecting the properties of a membrane, it is possible to control howforce from an indentor will be distributed over pressure sensors in apressure-sensitive structure. This can be very beneficial in someapplications.

SUMMARY OF THE INVENTION

In general, the invention relates to position sensing surfaces whereinindividual sensing elements located on a substrate measure pressure atspecific locations. In many cases it is desirable to know the locationof the applied pressure, which may not be directly over one of thesensing elements. In such applications, a membrane positioned adjacentthe substrate can distribute the pressure over several nearby pressuresensing elements, which enables one to compute the pressure at any pointby interpolating between sensors. This also provides a means to reducethe total number of sensing elements for a resulting reduction in costsand complexity.

The sensitivity of the device may be improved by the use of protrusionson the membrane, each of which is located so as to contact an individualsensing element. As can be imagined, when a membrane is constructed inthis manner, any force applied to the membrane is transferred to theindividual sensing elements by the protrusions. Since the total contactarea of the protrusions is small, the bearing pressure is concentratedat those protrusions.

If an “indentor” is used to apply a force to the surface, the locationof the indentor may be estimated by means of a centre-of-mass algorithmor other similar mathematical computation. The invention provides to animproved method to accurately compute the indentor location.

The invention further relates to a position sensor comprising asubstrate covered by a membrane. The substrate comprises an array ofpressure detecting means. The pressure detecting means may comprise anyof a number of systems, including force sensitive resistors,piezo-electric crystals, strain gauge-based sensors, and opticalpressure sensors of the type described in WO 99/04234, among others. Thetype of pressure detecting means may be varied without departing fromthe invention. One aspect of the invention relates to the use ofphysical features in the membrane (such as holes or recesses) to tailorthe distribution of pressure. Another aspect of this invention relatesto position sensors having irregular distributions of pressure sensingelements. Another aspect of this invention provides a way to accuratelycompute the location of an “indentor” which is applying pressure.

In one aspect, the invention comprises a position sensor, comprising asubstrate covered by a membrane. The substrate includes an array ofindividual pressure-detecting elements. The membrane has a non-uniformstructure and comprises means for isolating areas of depression of themembrane caused by local application of pressure wherein depression of afirst of said areas causes substantially no depression of a second,adjacent area.

The means for isolating the membrane areas may comprise a slot betweenthe first and second areas. Alternatively, the isolating means maycomprise an area in which the membrane is fixed to the substrate. Themembrane may be fixed to the substrate in a trough, or depressed portionbetween the areas. The portions of the membrane adjacent to the troughare not fixedly engaged to the substrate.

In one embodiment, the membrane comprises at least one depressed regionfor contacting the substrate. The membrane is separated from thesubstrate other than at the location at the at least one depressedregion.

The isolated membrane areas have various shapes and may be arranged inregular or irregular arrays. The areas may be one or more of arectangular, triangular, truncated triangular or irregular-shaped.

In another aspect, the membrane is partly separated from the substrate,being supported on the substrate by one or more regions of the membranewhich contact the substrate. Pressure applied to the membrane is thustransmitted to the substrate solely or substantially at the contactregions.

In another aspect, the invention comprises a pressure sensing surfacecomprising a substrate having an array of pressure sensing means andsignal processing means to receive pressure information from saidsensing means. The signal processor means is programmed to calculate thelocation and magnitude of force applied to the membrane according to aformulae described herein, in which the sensor is assumed to begenerally planar with x, y coordinates describing its surface.

This specification includes directional references such as “up” and“down” for convenience and ease of understanding. It will be understoodthat the sensors described herein may be placed in any orientation. Thedirectional references herein are not intended to be limit theinvention.

BRIEF DESCRIPTION OF DRAWINGS

In drawings which illustrate non-limiting embodiments of the invention:

FIG. 1 is a sectional profile view of a membrane system according to oneembodiment of the invention;

FIG. 2 is a plan view of a membrane system according to anotherembodiment of the invention;

FIG. 3 is a plan view of a membrane system according to a furtherembodiment of the invention;

FIG. 4 is a sectional profile view through the membrane system of FIG.3;

FIG. 5 is a plan view of a membrane system according to anotherembodiment of the invention;

FIG. 6 is a sectional view along the line A—A in FIG. 5; and,

FIG. 7 is a sectional view of a membrane system according to a stillfurther embodiment of the invention.

DESCRIPTION

Throughout the following description, specific details are set forth inorder to provide a more thorough understanding of the invention.However, the invention may be practiced without these particulars. Inother instances, well known elements have not been shown or described indetail to avoid unnecessarily obscuring the invention. Accordingly, thespecification and drawings are to be regarded in an illustrative, ratherthan a restrictive, sense.

A first aspect of the invention relates to constructions forpressure-sensitive devices. Anything which applies a downward force onthe surface of such a device is referred to herein as an “indentor”. Inmost applications it is of interest to be able to determine the locationand magnitude of force applied to a pressure-sensitive device by one ormore indentors.

FIG. 1 shows a membrane system 10 according to a first embodiment of theinvention. Membrane system 10 comprises a substrate 12, an overlyingflexible membrane 14 and a number of pressure sensors 20 which arelocated to detect forces applied by one or more indentors to membrane14.

Membrane 14 may be fabricated from a broad selection of materials andmay be fabricated by a variety of processes. Membrane 14 is preferablyflexible and elastic. The flexibility and modulus of elasticity ofmembrane 14 are determined by the material(s) from which membrane 14 ismade, the manufacturing processes used to make membrane 14, thethickness of membrane 14, and the shape of membrane 14. These parametersare referred to as “physical parameters” of membrane 14.

Membrane 14 may comprise a wear surface 16. Wear surface 16 may compriseone or more layers of material. Membrane 14 may serve severalpurposes—it provides a durable wear surface, it protects pressuresensors 20 from the environment and it can distribute applied pressuresover multiple sensors 20. Membrane 14 may be constructed so that itconcentrates applied forces over individual pressure sensors 20, therebyincreasing the sensitivity of system 10.

Wear surface 16 may provide an appropriate aesthetic or tactile nature.Wear surface 16 may comprise one or multiple layers. The one or morelayers may each comprise any of a wide variety of materials, includingpolyurethane, polyester, polycarbonate, rubber, fabric, leather, andalmost any other flexible material. In some cases, graphics may beprinted on layers of wear surface 16 or membrane 14. The layers of wearsurface 16 may be thick or thin, or of varying thickness. In someembodiments membrane 14 may include or overlie a layer of a compressiblematerial between wear surface 16 and substrate 12.

There are a plurality of pressure sensors 20 on substrate 12. Pressuresensors 20 may comprise individual pressure sensors, or, may comprise adistributed pressure sensor such as the cellular-type pressure sensordescribed in WO 00/73982. A pressure sensing arrangement of this typecomprises a pad made of a compressible medium such as, cellular foam,which is semi-transparent or translucent to light. Compression of themedium alters the intensity of light detected by light sensors in anarray of optical sensors. A signal processing unit translates theresulting signal into a determination of the location of force appliedto the pressure sensing surface. The optical components and signalprocessing unit are not shown herein, but are fully described in WO00/73982, which is incorporated herein by reference.

The specific type of pressure sensor 20 is not an essential aspect ofthe invention. Pressure sensors 20 may comprise sensors which measuredeflection, forces or pressure. Pressure sensors 20 may compriseforce-sensitive resistor elements. A sensor which can be used to senseforces applied to membrane 14 is referred to herein as a “pressuresensor”, whatever the fundamental nature or mode of operation of thesensor may be. Pressure sensors 20 may be arranged in a regular array,such as a rectangular array or a hexagonal or triangular array. In someembodiments, pressure sensors 20 may be irregularly distributed onsubstrate 12.

The physical properties of membrane 14 may be selected and made to varyacross membrane 14 in ways which alter the manner in which forcesapplied by indentors pressing on the upper surface 17 of membrane 14 aretransmitted to sensors 20.

In the embodiment of FIG. 1, membrane 14 is substantially flat and hasprotrusions 18 formed on its underside 15 (the side adjacent substrate12). Protrusions 18 are positioned to overlie individual pressuresensors 20. Protrusions 18 contact pressure sensors 20. Elsewhere thereis a space 21 between substrate 12 and underside 15 of membrane 14.Protrusions 18 may optionally be adhered to pressure sensors 20.

Forces applied to the upper surface of membrane 14 are distributed topressure sensors 20 by way of protrusions 18. Protrusions 18 concentratedownward forces applied to surface 16 over a subset of pressure sensors20. This increases the sensitivity of system 10 and, by distributing thepressure over a number of pressure sensors 20, it facilitates accuratedetermination of the locations of applied forces.

Protrusions 18 may have various configurations. Protrusions 18 mayinclude bumps which may be circular or other shaped, or straight orcurved ridges. Protrusions may also be provided on top surface 17 ofmembrane 14. The protrusions typically increase the stiffness ofmembrane 14. Membrane 14 may also, or in the alternative, comprise areasof weakness. Areas of weakness may be provided by cuts or holes in themembrane, recessed regions, regions in which the membrane is made of adifferent material or composition, or regions in which one or morelayers of the membrane are not present, are of different thickness, etc.The thickness of membrane 14 may vary over its area.

In some applications, it is desirable to provide a membrane systemdivided into two or more separate areas, each of which can independentlymeasure the location(s) and force(s) applied to the area by one or moreindentors. FIG. 2 illustrates a membrane system 10, comprising substrate12 overlain by membrane 14. Membrane 14 is divided into two areas 24 aand 24 b by a divider 22. In the FIG. 2 embodiment, divider 22 comprisesa slot 23. Because membrane 14 is interrupted by slot 23, it does notdistribute applied force from one area 24 to the other. Due to thediscontinuity in membrane 14, indentors applying force in area 24 a haveno effect on the pressure signals generated by sensors 20 associatedwith area 24 b, and vice versa. A membrane system 10 according to theinvention may be divided into a plurality of separate areas of desiredsizes and shapes by providing suitable dividers 22.

Dividers 22 may be formed by one or more of slots or other weakenedregions within membrane 14 and regions of membrane 14 which contactsubstrate 12. Regions which contact substrate 12 may be trough-like inshape to isolate separate regions on either side of the trough. In thealternative, in these regions, membrane 14 may have bumps, ridges, orother protrusions which contact substrate 12.

FIGS. 3 and 4 illustrate a further embodiment in which membrane 14 isdivided into separate areas. In this embodiment, divider 22 comprises aregion 30. In region 30 membrane 14 is adhered to substrate 12. Region30 divides membrane 14 into two areas. Firmly affixing membrane 14 tosubstrate 12 between areas 32 a and 32 b prevents vertical forces frombeing transmitted from one area to an adjacent area. This isolates theareas. Divider 22 also affects the distribution of forces among pressuresensors 20 associated with areas 32. Where divider 22 comprises recessedregion 30, recessed region 30 supports some applied load, andeffectively stiffens membrane 14 near edges of areas 32 a and 32 b. Incertain applications this can be used to advantage.

Dividers 22 may be designed in an application-specific manner. Forexample, consider an application wherein a touch surface is to bedivided into two separate areas along its length (see FIG. 3) byrecessed regions 30. In this example, touching within area 32 a will notaffect sensors in the adjacent area 32 b. By constructing membrane 14with recessed regions 30 (which are firmly fixed to substrate 12) alongthe long edges of areas 32 a and 32 b, membrane 14 is made to be morerigid. This provides an additional effect: the distribution of forcesalong the length of each area 32 (i.e. within each area 32) isdiminished. As a result, pressure sensors 20 within each area 32 arealso de-coupled (to some extent), even though there is not a physicalfeature dividing pressure sensors 20 within either area 32.

Consider another application where a touch surface is to be dividedalong its length by slot 23 as in FIG. 2. Like areas 32 a and 32 b,areas 24 a and 24 b, separated by slot 23, are isolated in that forceapplied to one area has no effect on the other area. However, each area24 a and 24 b provides a continuous sensory surface. Several pressuresensors 20 respond to force applied on an indentor placed anywhere ineither area.

The pressure distribution of membrane 14 can be tailored for specificapplications. A combination of physical features (holes, slots, recessedregions, protrusions, bumps, ridges, varying thickness, etc.) may beused to achieve a variety of performance characteristics. One can thinkof these physical features as a set of tools to be used to create thedesired performance characteristics.

In some cases, a regular, rectangular arrangement of pressure sensors 20is preferred. In other applications, however, pressure sensors 20 may bearranged irregularly. The distribution of force by an indentor appliedto pressure sensors 20 is determined by the physical parameters ofmembrane 14 (as described above). In combination with careful design ofthe physical parameters, the number of pressure sensors 20 may beminimized while still achieving a desired performance.

FIGS. 5 and 6 illustrate a membrane system 10 according to analternative embodiment of the invention. Membrane system 10 comprisessubstrate 12 covered by membrane 14. Membrane 14 is divided into areas31 of various shapes and orientations by a combination of recessedregions 30 and slots 23. Isolated areas 31 may comprise rectangles,truncated triangles and various irregular shapes. The arrangementillustrated in FIG. 5 is only an example and is not intended to belimiting. Many arrangements of areas 31 may be defined within membrane14.

FIG. 7 shows a membrane system 10 according to a further embodiment ofthe invention. In the embodiment of FIG. 7, substrate 12 comprises anumber of cells 40. Each cell 40 comprises an optical cavity 42 filledwith a pressure-sensitive medium 44. Cells 40 are arranged to defineisolated areas 46 a and 46 b of the overlying membrane 14. Pressuredetecting means are provided in each area 46. The pressure detectingmeans may comprise a plurality of optical receiver/transmitter pairs 48positioned in each cavity 42 underneath pressure-sensitive medium 44.Areas 46 a and 46 b are isolated from one another by isolating means. Inthe embodiment illustrated in FIG. 7, the isolating means comprises theportion 50 of membrane 14 attached to substrate 12 between cavities 42.

Any one of the membrane systems described above may be combined with acontroller which derives information about the location and forceapplied to membrane 14 by one or more indentors from the signalsgenerated by pressure sensors 20. The controller may provide outputswhich identify the locations of one or more indentors in a suitableone-dimensional or two-dimensional coordinate system. The controller mayalso provide outputs which indicate the magnitude of the forces beingapplied at the locations of the indentor(s).

It is often desirable to know the location at which an indentor appliespressure to membrane system 10. Consider the case of an indentorapplying a force upon membrane 14. In some prior art pressure sensors,the location of an indentor is determined by computing the“centre-of-mass” of the pressure signals. The process can be generalizedto compute the locations of several indentors by a variety of differentalgorithms which determine a subset of pressure sensors corresponding toeach indentor; a centre-of-mass or similar algorithm is then used oneach subset to compute the location of the corresponding indentor. It isgenerally accepted that, for accurate centre-of-mass calculation, thesensors should be located in a regular rectangular array. Thatrestriction is not necessary for this invention.

The pressure signal from a (properly calibrated) pressure sensor 20depends on the force applied to membrane 14 and the distance from thecentre of the indentor to the pressure sensor 20 as follows:v _(i) =V(w,r _(i))  (1)where v_(i) is the pressure signal of the i^(th) sensor, w is thedownward force applied by the indentor and r_(i) is the distance fromthe indentor to the i^(th) sensor. The inventors have determined thatthe function V can be represented as a product of two functions, onedependent only on w, and the other dependent on the distance between theindentor and the sensor as follows:V(w,r _(i))=V _(w)(w)V _(r,i)(r _(i))  (2)where V_(w) is a function which depends only on the force applied andV_(r,i) is a function which depends only on the distance. Pressuresensors 20 are preferably chosen such that the function V_(w)(w) is thesame for all sensors. The function V_(r,i)(r_(i)) may be different foreach sensor, depending on the physical features of membrane 14. Tocalibrate membrane system 10, one applies a number of known forces to anumber of known locations on membrane 14 and measures v_(i) from eachpressure sensor 20 for each known force. Well known numerical methodsare then used to determine V_(w)(w) and V_(r,i)(r_(i)).

The following examples relate to systems comprising a pressure-sensitivesurface comprising an array of individual sensor elements, and acontroller for receiving pressure information from the sensor elements.The controller is programmed to determine the location and optionallythe amount of pressure applied by an indentor to the pressure-sensitivesurface with a high degree of precision. The examples relate to variousspecific sensor arrays and controller functions.

EXAMPLE 1 Computing the Location of Applied Pressure

Consider a pressure-sensitive surface comprising a single straight rowof sensors, onto which a membrane is applied. The coordinate x is usedto specify the distance along an axis through the centers of the sensorsfrom an arbitrary origin. In this example, the distance between theindentor and a sensor is simply r_(i)=x−x_(i), where x is the locationof the indentor and x_(i) is the location of sensor i.

The problem is to determine the location x and the applied force w, forknown set of v_(i), and x_(i), i=1, . . . , N. One could compute thelocation x by the following formula:

$\begin{matrix}{{x \approx \hat{x}} = \frac{\sum\limits_{i = 1}^{N}\;{x_{i}v_{i}}}{\sum\limits_{i = 1}^{N}\; v_{i}}} & (3)\end{matrix}$where {circumflex over (x)} is the estimated value of x. Equation (3)explicitly depends on the locations of the sensors, x_(i), andimplicitly depends on the physical parameters of the membrane. As aresult, in general x≠{circumflex over (x)}. Another way of stating thisis that due to the shape of the function V_(r,i), {circumflex over (x)}may not be an accurate estimate of x.

This invention provides a method for accurately determining x. Thefollowing is the mathematical basis for this aspect of the invention.Substituting Equations (1) and (2) into Equation (3) yields:

$\begin{matrix}{\hat{x} = {\frac{\sum\limits_{i = 1}^{N}\;{x_{i}{V_{w}(w)}{V_{r,i}\left( {x - x_{i}} \right)}}}{\sum\limits_{i = 1}^{N}\;{{V_{w}(w)}{V_{r,i}\left( {x - x_{i}} \right)}}} = \frac{\sum\limits_{i = 1}^{N}\;{x_{i}{V_{r,i}\left( {x - x_{i}} \right)}}}{\sum\limits_{i = 1}^{N}\;{V_{r,i}\left( {x - x_{i}} \right)}}}} & (4)\end{matrix}$where V_(w)(w) has been removed from the summation since it does notdepend on i. As a result of Equation (2), the estimated location,{circumflex over (x)}, does not depend on the applied force. Forconvenience, we define the function h(x) as:

$\begin{matrix}{{h(x)} \equiv \frac{\sum\limits_{i = 1}^{N}\;{x_{i}{V_{r,i}\left( {x - x_{i}} \right)}}}{\sum\limits_{i = 1}^{N}\;{V_{r,i}\left( {x - x_{i}} \right)}}} & (5)\end{matrix}$

One can define the inverse of h(x) to be the function H as follows:H(h(x))=x  (6)

H can be determined experimentally by acquiring pressure signals fromsensors 20 as a known force is applied to membrane 14 at variouspositions along the x-direction. The acquired data may be used tocompute {circumflex over (X)} as a function of x. Inverting thefunctional dependence yields x as a function of {circumflex over (X)},which is the function H.

One could also determine H numerically by applying Equations (5) and (6)using analytical expressions for the function V_(r,i). Since H isindependent of w, it is dependent only on the physical parameters andthe geometry of membrane 14, so it needs to be determined only once.i.e. it can be determined in advance of use and called upon as requiredin an application. Having determined the function H, one can determinethe location of an indentor by computing {circumflex over (x)} byEquation (3) and then computing x as follows:x=H({circumflex over (x)})  (7)where x is the solution to the problem which was posed.

To summarize, one can compute x by application of the followingalgorithm:

-   -   determine the function H beforehand, by experimentation or        analysis and store a representation of H;    -   during operation compute {circumflex over (x)} from known v_(i)        and x_(i), by Equation (3); and,    -   during operation determine x by computing x=H({circumflex over        (x)}).

H may be stored as a function, a lookup table containing values atrepresentative points of H, as a set of parameters which defines afunction which approximates H—e.g. a set of polynomial coefficients, orthe like.

To determine the magnitude of the applied force, one takes the sum ofthe pressure signals:

$\begin{matrix}{{\sum\limits_{i = 1}^{N}\; v_{i}} = {{\sum\limits_{i = 1}^{N}\;{{V_{w}(w)}{V_{r,i}\left( {x - x_{i}} \right)}}} = {{V_{w}(w)}{\sum\limits_{i = 1}^{N}\;{V_{r,i}\left( {x - x_{i}} \right)}}}}} & (8)\end{matrix}$

This expression could be used as an estimate of the applied force, w.However, Σv_(i) is dependent on x. Thus the same applied force canresult in different computed values of Σv_(i), depending on the locationof the indentor. To facilitate computation of the applied force, w, wedefine the function:

$\begin{matrix}{{W(w)} \equiv \frac{V_{w}(w)}{V_{w}\left( w_{0} \right)}} & (9)\end{matrix}$where w₀ is a specified (constant) applied force. Rearranging this andsubstituting it into Equation (8), yields:

$\begin{matrix}{{\sum\limits_{i = 1}^{N}v_{i}} = {{{W(w)}{V_{w}\left( w_{0} \right)}{\sum\limits_{i = 1}^{N}{V_{r,i}\left( {x - x_{i}} \right)}}} = {{W(w)}\left\lbrack {\sum\limits_{i = 1}^{N}v_{i}} \right\rbrack}_{w = w_{0}}}} & (10)\end{matrix}$

The function ƒ(x) is defined as follows:

$\begin{matrix}{{f(x)} \equiv \left\lbrack {\sum\limits_{i = 1}^{N}{\cdot v_{i}}} \right\rbrack_{w = w_{0}}} & (11)\end{matrix}$which depends only on x, since the summation is evaluated at a knownforce w₀. Inherent in ƒ(x) are the geometric and physical parameters ofthe membrane. In practice, ƒ(x) can easily be determined by applyingforce w₀ to the membrane with an indentor at a number of positions x,and computing the sum of the sensor responses for each position of theindentor. The relationship between the position x and the sum ofresponses (for force w₀) is the function ƒ(x).

Alternatively, if a mathematical model of the sensor response is known,then the function ƒ(x) may be determined analytically or numerically.The function ƒ(x) need only be determined once and may be called upon asrequired during operation. Having determined the function ƒ(x), andhaving computed x previously, computation of the function W(w) followsby application of Equation (8) as follows:

$\begin{matrix}{{W(w)} = \frac{\sum\limits_{i = 1}^{N}v_{i}}{f(x)}} & (12)\end{matrix}$

Importantly, W(w) does not depend on the coordinates of the indentorbecause of the assumption of Equation (2) and the definition of W(w).Even though the indentor position is used in the computation of ƒ(x),and therefore in the computation of W(w), the division of Σv_(i) by ƒ(x)exactly counteracts any positional dependency in Σv_(i).

In practice, knowing the value of W is generally sufficient since W is asingle-valued monotonic function of w. However, in applications where itis important to know w exactly, then the function V_(w)(w) of Equation(9) can be inserted and the inverted function used to compute w asfollows:w=V _(w) ⁻¹(W(w)V _(w)(w ₀))  (13)where V_(w) ⁻¹(W) is the inverse of V_(w)(w).

EXAMPLE 2 Computation for an x-y-pad

Consider a two-dimensional pressure-sensitive surface whereupon we wishto compute the location of the indentor in two dimensions using aCartesian coordinate system. The method described here can also beapplied for other frames of reference. An indentor applies a downwardforce of magnitude w at coordinates (x,y). As before, we assume that thepressure response of the sensors satisfies Equation (2). In this case,however, the distance r is given by:r _(i)=√{square root over ((x−x _(i))²+(y−y _(i))²)}{square root over((x−x _(i))²+(y−y _(i))²)}  (14)where (x_(i),y_(i)) are the coordinates of sensor i.

The location of the indentor could be computed as follows:

$\begin{matrix}{\hat{x} = \frac{\sum\limits_{i}{x_{i}v_{i}}}{\sum\limits_{i}v_{i}}} & (15) \\{\hat{y} = \frac{\sum\limits_{i}{y_{i}v_{i}}}{\sum\limits_{i}v_{i}}} & (16)\end{matrix}$

However, in general, {circumflex over (x)} and ŷ will not accuratelydetermine x and y. In general, {circumflex over (X)} will differ from xby an amount that depends on x and y.

This invention provides a method for accurately determining x and y.Substituting Equation (2) into Equation (15) and (16) and simplifyingyields:

$\begin{matrix}{\hat{x} = \frac{\sum\limits_{i}{x_{i}{V_{r,i}\left( r_{i} \right)}}}{\sum\limits_{i}{V_{r,i}\left( r_{i} \right)}}} & (17) \\{\hat{y} = \frac{\sum\limits_{i}{y_{i}{V_{r,i}\left( r_{i} \right)}}}{\sum\limits_{i}{V_{r,i}\left( r_{i} \right)}}} & (18)\end{matrix}$

V_(w)(w) is independent of i and can therefore be removed from thesummation. Equations (17) and (18) show that, under the assumption ofEquation (2), both {circumflex over (x)} and ŷ are independent of theapplied force. The functions h(x,y) and g(x,y) are defined as follows:

$\begin{matrix}{\hat{x} = {{h\left( {x,y} \right)} \equiv \frac{\sum\limits_{i}{x_{i}{V_{r,i}\left( r_{i} \right)}}}{\sum\limits_{i}{V_{r,i}\left( r_{i} \right)}}}} & (19) \\{\hat{y} = {{g\left( {x,y} \right)} \equiv \frac{\sum\limits_{i}{y_{i}{V_{r,i}\left( r_{i} \right)}}}{\sum\limits_{i}{V_{r,i}\left( r_{i} \right)}}}} & (20)\end{matrix}$The system of Equations (19) and (20) is then solved for (x,y) in termsof ({circumflex over (x)},ŷ). The functions H and G are defined asfollows:x=H({circumflex over (x)},ŷ)y=G({circumflex over (x)},ŷ)  (21)

As with Example 1, if an exact mathematical model of the pressureresponse is known, the functions H and G may be determined analyticallyor numerically. It is straightforward in practice to determine H and Gexperimentally. This can be done by applying a downward force to themembrane at a number of known positions (x,y), and computing({circumflex over (x)},ŷ) for each of the known positions from theresponses of the pressure sensors when the downward force is beingapplied at those known positions. The relationship between x and({circumflex over (x)},ŷ) is H, and the relationship between y and({circumflex over (x)},ŷ) is G. The relationships H and G need only bedetermined once for a given design of pressure sensing surface—they aredependent on the geometry and physical parameters of the membrane.Having determined the functions H and G, the coordinates of the indentorlocation can be determined during operation by computing ({circumflexover (x)},ŷ) in accordance with Equation (15) and (16) and then applyingEquation (21).

It remains to compute the magnitude of the applied force. This follows asimilar derivation as in Example 1. First define the parameter W(w) asin Equation (9). W(w) does not depend on the location (x,y) of theindentor. Rearranging Equation (9), yields V_(w)(w)=W(w)V_(w)(w₀).Substituting this and Equation (2) into Equation (15) yields aftersimplification:

$\begin{matrix}{{\sum\limits_{i}v_{i}} = {{W(w)}\left\lbrack {\sum\limits_{i}v_{i}} \right\rbrack}_{w = w_{0}}} & (22)\end{matrix}$which is identical to Equation (10). One then defines a new function:

$\begin{matrix}{{f\left( {x,y} \right)} \equiv \left\lbrack {\sum\limits_{i}v_{i}} \right\rbrack_{w = w_{0}}} & (23)\end{matrix}$

ƒ(x,y) is dependent only on the coordinates (x,y) of the indentor sincethe summation is evaluated at a known force w₀. Inherent in ƒ(x,y) arethe geometric and physical parameters of the membrane. In practice,ƒ(x,y) can easily be determined by applying force w₀ to the membranewith an indentor at a number of known positions (x,y) and computing thesum of the sensor responses. The relationship between the position (x,y)and the sum of responses (for force w₀) is the function ƒ(x,y).Alternatively, if a mathematical model of the sensor response, Equation(1) is known, then ƒ(x,y) may be determined analytically or numerically.ƒ(x,y) need only be determined once and may be called upon as requiredduring operation. Having determined ƒ(x,y), and having computed (x,y)previously, computation of the applied force follows by application ofEquation (22) as follows:

$\begin{matrix}{{W(w)} = \frac{\sum\limits_{i}v_{i}}{f\left( {x,y} \right)}} & (24)\end{matrix}$

In practice, knowing the value of W(w) is generally sufficient since itis a single-valued monotonic function of w. Importantly, W(w) does notdepend on the location of the indentor (even though knowledge of thosecoordinates was used to compute ƒ(x,y)). In essence, division by ƒ(x,y)exactly counteracts the positional dependency of

$\sum\limits_{i}{v_{i}.}$

In applications where it is important to know w exactly, then thefunction W(w) can be inverted and the inverted function used to computew. In order to do this, an analytic or numerical model for V_(w)(w) isrequired, and then the definition of W(w), Equation (9), can be appliedas follows:w=V _(w) ⁻¹(W(w)V _(w)(w ₀))  (25)where V_(w) ⁻¹(W) is the inverse of V_(w)(w).

EXAMPLE 3 Special Case of an xy-pad with Row-column Sensor Arrangement

Consider the case where the pressure sensors have been arranged in aseries of straight rows and straight columns. For convenience we chosethe coordinate frame of reference, F_(xy), to be oriented along the rowsand columns. It is not necessary that the rows and columns be equallyspaced, but it is stipulated that the pressure sensors are located atthe every intersection of the imaginary straight lines which representthe rows and columns.

For this example, we introduce another assumption: the functionV_(r)(x,y) can be separated into the product of two functions asfollows:V _(r)(r)=V _(x)(Δx)V _(y)(Δy)  (26)where r is related to Δx and Δy by r=√{square root over (Δx²+Δy²)}.Expanding Equation (2) with this assumption yields:V(w,r)=V _(w)(w)V _(x)(Δx)V _(y)(Δy)  (27)

In terms of an individual sensor response, this is written asv _(i) =V(w,r _(i))=V _(w)(w)V _(x,i)(Δx _(i))V _(y,i)(Δy _(i))  (28)where v_(i), is the pressure signal of sensor i located at coordinates(x_(i),y_(i)), w the downward force applied by an indentor atcoordinates (x,y), and (Δx_(i),Δy_(i)) is the difference in coordinatesbetween the sensor and the indentor: Δx_(i)=x−x_(i), Δy_(i)=y−y_(i). Itcan be verified by experimentation that touch sensitive surfacesfabricated in accordance with the foregoing do in fact satisfy Equation(28) to very close approximations.

Substituting Equation (28) into Equation (15) and simplifying yields:

$\begin{matrix}{\hat{x} = \frac{\sum\limits_{i}{x_{i}{V_{x,i}\left( {\Delta\; x_{i}} \right)}{V_{y,i}\left( {\Delta\; y_{i}} \right)}}}{\sum\limits_{i}{{V_{x,i}\left( {\Delta\; x_{i}} \right)}{V_{y,i}\left( {\Delta\; y_{i}} \right)}}}} & (29)\end{matrix}$

Since the sensors are arranged regularly, it follows that for each rowof sensors, y_(i)=y_(j), for sensors i, j in the same row. SoV_(y)(Δy_(i))=V_(y)(Δy_(j)) for sensors in the same row. Then:

$\begin{matrix}\begin{matrix}{\hat{x} = \frac{\begin{matrix}{{\sum\limits_{Row1}{x_{i}{V_{x,i}\left( {\Delta\; x_{i}} \right)}{V_{y\;,i}\left( {\Delta\; y_{i}} \right)}}} + {\sum\limits_{Row2}{x_{i}{V_{x,i}\left( {\Delta\; x_{i}} \right)}{V_{y\;,i}\left( {\Delta\; y_{i}} \right)}}} + \ldots +} \\{\sum\limits_{RowM}{x_{i}{V_{x,i}\left( {\Delta\; x_{i}} \right)}{V_{y\;,i}\left( {\Delta\; y_{i}} \right)}}}\end{matrix}}{\begin{matrix}{{\sum\limits_{Row1}{{V_{x,i}\left( {\Delta\; x_{i}} \right)}{V_{y\;,i}\left( {\Delta\; y_{i}} \right)}}} + {\sum\limits_{Row2}{{V_{x,i}\left( {\Delta\; x_{i}} \right)}{V_{y\;,i}\left( {\Delta\; y_{i}} \right)}}} + \ldots +} \\{\sum\limits_{RowM}{{V_{x,i}\left( {\Delta\; x_{i}} \right)}{V_{y\;,i}\left( {\Delta\; y_{i}} \right)}}}\end{matrix}}} \\{= \frac{V_{y}{_{Row1}{{\sum\limits_{Row1}{x_{i}{V_{x,i}\left( {\Delta\; x_{i}} \right)}}} + \ldots + V_{y}}}_{RowM}{\sum\limits_{RowM}{x_{i}{V_{x,i}\left( {\Delta\; x_{i}} \right)}}}}{V_{y}{_{Row1}{{\sum\limits_{Row2}{V_{x,i}\left( {\Delta\; x_{i}} \right)}} + \ldots + V_{y}}}_{RowM}{\sum\limits_{RowM}{V_{x,i}\left( {\Delta\; x_{i}} \right)}}}}\end{matrix} & (30)\end{matrix}$where V_(y)|_(RowK) is the value of V_(y)(Δy_(i)) for any sensor locatedin row K. Since the sensors are arranged regularly, it follows that

${\sum\limits_{RowK}{x_{i}{V_{x,i}\left( {\Delta\; x_{i}} \right)}}} = {{\sum\limits_{RowL}{x_{i}{V_{x,i}\left( {\Delta\; x_{i}} \right)}\mspace{14mu}{and}\mspace{14mu}{\sum\limits_{RowK}{V_{x,i}\left( {\Delta\; x_{i}} \right)}}}} = {\sum\limits_{RowL}{V_{x,i}\left( {\Delta\; x_{i}} \right)}}}$for all rows K, L. Therefore:

$\begin{matrix}\begin{matrix}{\hat{x} = \frac{\left\{ \left. V_{y} \middle| {}_{Row1}{+ V_{y}} \middle| {}_{Row2}{{+ \ldots} + V_{y}} \right|_{RowM} \right\}\left\{ {\sum\limits_{Row1}{x_{i}{V_{x,i}\left( {\Delta\; x_{i}} \right)}}} \right\}}{\left\{ \left. V_{y} \middle| {}_{Row1}{+ V_{y}} \middle| {}_{Row2}{{+ \ldots} + V_{y}} \right|_{RowM} \right\}\left\{ {\sum\limits_{Row1}{V_{x,i}\left( {\Delta\; x_{i}} \right)}} \right\}}} \\{= \frac{\sum\limits_{Row1}{x_{i}{V_{x,i}\left( {\Delta\; x_{i}} \right)}}}{\sum\limits_{Row1}{V_{x,i}\left( {\Delta\; x_{i}} \right)}}}\end{matrix} & (31)\end{matrix}$In a similar manner, one derives:

$\begin{matrix}{\hat{y} = \frac{\sum\limits_{Column1}{y_{i}{V_{y\;,i}\left( {\Delta\; y_{i}} \right)}}}{\sum\limits_{Column1}{V_{y\;,i}\left( {\Delta\; y_{i}} \right)}}} & (32)\end{matrix}$

Equations (31) and (32) show that under assumption (28), {circumflexover (x)} is independent of the y-coordinate of the indentor and ŷ isindependent of the x-coordinate of the indentor. Both {circumflex over(x)} and ŷ are independent of the applied force. One thus writes:{circumflex over (x)}=h(x)ŷ=g(y)  (33)where h(x) and g(x) are defined to be the right-hand sides of Equations(31) and (32) respectively. Let us assume that we can invert thefunctions h(x) and g(x). That is, define the functions H and G asfollows:H(h(x))=xG(g(y))=y

As with the one-dimensional case of Example 1, it is straightforward inpractice to determine H and G experimentally. Then, knowing H and G, onedetermines (x,y) by:x=H({circumflex over (x)})y=G({circumflex over (y)})  (34)

The system of equations (34) is much simpler that the correspondingsystem (21) for a general 2-dimensional surface. This example has shownthat for pressure-sensitive surfaces constructed with straight rows andcolumns of sensors (even if they are not equally spaced), thecomputation of the location of the indentor is simplified by use ofEquation (34) rather than Equation (21). Determination of the appliedforce follows in exactly the same manner as in the general case ofExample 2.

The foregoing methods may be performed in a controller comprising aprogrammed data processor. The data processor could comprise, forexample, one or more microprocessors. The one or more processors in thecontroller may implement the methods of the invention by executingsoftware instructions in a program memory accessible to the one or moreprocessors. Calibration information including a representation of H and,where appropriate, G may be stored in a data store in or otherwiseaccessible to the controller.

The invention has a wide range of possible applications including keypads for electronic equipment, controllers for electronic musicalequipment, and the like.

The invention may also be provided in the form of a program product. Theprogram product may comprise any medium which carries a set ofcomputer-readable signals comprising instructions which, when executedby a computer processor, cause the data processor to execute a method ofthe invention. Program products according to the invention may be in anyof a wide variety of forms. The program product may comprise, forexample, physical media such as magnetic data storage media includingfloppy diskettes, hard disk drives, optical data storage media includingCD ROMs, DVDs, electronic data storage media including ROMs, flash RAM,or the like or transmission-type media such as digital or analogcommunication links.

Where a component (e.g. a software module, processor, assembly, device,circuit, etc.) is referred to above, unless otherwise indicated,reference to that component (including a reference to a “means”) shouldbe interpreted as including as equivalents of that component anycomponent which performs the function of the described component (i.e.,that is functionally equivalent), including components which are notstructurally equivalent to the disclosed structure which performs thefunction in the illustrated exemplary embodiments of the invention.

As will be apparent to those skilled in the art in the light of theforegoing disclosure, many alterations and modifications are possible inthe practice of this invention without departing from the spirit orscope thereof. For example, the novel methods for locating a position atwhich an indentor contacts a surface of a pressure-sensitive devicedescribed herein may be applied with types of pressure-sensitivestructure other than those described in the preceding description. Thesemethods may also be applied to locate points at which indentor(s)contact certain prior art pressure-sensitive devices. The methods fordetermining a magnitude of a force applied to an indentor may also beused with pressure-sensitive devices other than those described in thepreceding description including certain prior art pressure-sensitivedevices. Accordingly, the scope of the invention is to be construed inaccordance with the substance defined by the following claims.

1. A position sensor comprising a substrate covered by a membrane and aplurality of pressure sensors on the substrate, the membrane comprisingat least first and second areas separated by at least one divider,wherein a force applied to the first area causes substantially noresponse in those of the pressure sensors underlying the second areawherein the membrane has a stiffness which varies with position on themembrane.
 2. The position sensor according to claim 1, wherein the atleast one divider comprises a slot in the membrane.
 3. The positionsensor according to claim 2, wherein the membrane comprises protrusions,each protrusion positioned to contact a pressure sensor of the pluralityof pressure sensors.
 4. The position sensor according to claim 1,wherein the at least one divider comprises a region of the membraneattached to the substrate.
 5. The position sensor according to claim 4,wherein the membrane comprises protrusions, each protrusion positionedto contact a pressure sensor of the plurality of pressure sensors. 6.The position sensor according to claim 1 wherein the membrane comprisesa plurality of first areas wherein the stiffness of the membrane is atleast a first stiffness and a second area between two of the pluralityof first areas wherein the membrane has a stiffness less than the firststiffness.
 7. The position sensor according to claim 1 wherein themembrane comprises a plurality of first areas wherein the stiffness ofthe membrane does not exceed a first stiffness and a second area betweentwo of the plurality of first areas wherein the membrane has a stiffnessof at least the first stiffness.
 8. The position sensor according toclaim 1, wherein the substrate comprises a plurality of cavities and theat least one divider comprises at least one portion of the membraneattached to the substrate in a region between two of the plurality ofcavities.
 9. The position sensor according to claim 1, wherein themembrane is separated from the substrate except in at least one regionof the membrane wherein the membrane is in contact with the substrate.10. The position sensor according to claim 1, wherein the membranecomprises protrusions, each protrusion positioned to contact a pressuresensor of the plurality of pressure sensors.
 11. The position sensoraccording to claim 1 wherein the first and second areas are arranged ina non-regular array.
 12. The position sensor according to claim 1wherein the first and second areas are arranged in a regular array. 13.A position sensor comprising a substrate covered by a membrane and aplurality of pressure sensors on the substrate, the membrane comprisingat least first and second areas separated by at least one divider,wherein a force applied to the first area causes substantially noresponse in those of the pressure sensors underlying the second area andthe at least one divider comprises a weakened portion of the membrane.14. The position sensor according to claim 13, wherein the membrane isseparated from the substrate except in at least one region of themembrane wherein the membrane is in contact with the substrate.
 15. Theposition sensor according to claim 13, wherein the membrane comprisesprotrusions, each protrusion positioned to contact a pressure sensor ofthe plurality of pressure sensors.
 16. The position sensor according toclaim 13 wherein the first and second areas are arranged in anon-regular array.
 17. The position sensor according to claim 13 whereinthe first and second areas are arranged in a regular array.
 18. Theposition sensor according to claim 13 wherein the first and second areascomprise one or more of a rectangular, triangular, or truncatedtriangular area.